金融网络的双曲几何
The hyperbolic geometry of financial networks
摘要：
基于2014年、2016年欧洲银行业压力测试和2018年透明度测试的数据，我们首次证明了金融网络的潜在几何结构可以很好地用负曲率几何结构来表示，即，双曲几何这使我们能够将网络结构与Pappdopoulos等人的流行性与相似性模型联系起来，它是基于双曲几何的庞加莱圆盘模型。我们发现，在这个模型中的潜在维度的“流行性”和“相似性”是密切相关的系统的重要性和地理细分的银行系统。在2014年至2018年的纵向分析中，我们发现单个银行的系统重要性保持相当稳定，而外围社区结构表现出更多（但仍然适度）的变化。
英文摘要：
Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we demonstrate for the first time that the latent geometry of financial networks can be well-represented by geometry of negative curvature, i.e., by hyperbolic geometry. This allows us to connect the network structure to the popularity-vs-similarity model of Papdopoulos et al., which is based on the Poincaré disc model of hyperbolic geometry. We show that the latent dimensions of `popularity' and `similarity' in this model are strongly associated to systemic importance and to geographic subdivisions of the banking system. In a longitudinal analysis over the time span from 2014 to 2018 we find that the systemic importance of individual banks has remained rather stable, while the peripheral community structure exhibits more (but still moderate) variability.
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